Border Patrol stations like the ones in Brownsville and Nogales, both in Arizona, were not meant for long-term custody. Immigrants are supposed to wait there until they are processed and taken to detention centers, but the surge in children arriving without their parents has overwhelmed the U.S. government.

The U.S. Border Patrol is not the only federal agency overwhelmed by the huge influx of undocumented minors at the U.S.-Mexico border.

The Department of Health and Human Services, which had expected its greatest task at the time to be dealing with the disastrous rollout of the Affordable Care Act, is scrambling to care for and provide services to the tens of thousands of unaccompanied children coming to the United States from Central America.

Many are coming from Honduras, Guatemala and El Salvador, either fleeing violence in those countries, or seeking to reunite with parents or other relatives here, authorities say. About 50,000 have come within the past year.

The children are first put in the custody of the U.S. Border Patrol and then are handed over to HHS within 72 hours.

HHS takes them into one of several immigration shelters in various states – the administration said it is looking for more facilities to send the children. The agency is tasked with providing the children with services that include medical care, food, clothing, socialization and recreation, according to the HHS website.

The influx of children is straining the program – called Unaccompanied Alien Children (UAC) – which was meant to serve some 8,000 children a year while their cases were pending in immigration court, say representatives of child advocacy groups.

“The system as it was created was never meant to hold this many children,” said Megan McKenna, communications and advocacy director of Kids in Need of Defense (KIND), in an interview with Fox News Latino. “We’re very concerned that these children, who would like to claim U.S. protection and who are potentially eligible for U.S. protection are not able to access our system” for proper guidance on their rights and criteria for staying in the country.

Once in HHS custody, the agency then works to locate a parent or other relative with whom the child can stay. Some also stay in foster care.

Some child advocacy groups, including KIND, are assisting the government by doing such things as helping to provide basic necessities to the children, as well as guidance on what immigration relief may apply to them.

Human rights groups and lawyers who have spoken to many of the children estimate that between 60 to 80 percent of them could qualify for political asylum or a special visa for unaccompanied children who are deemed to have been abandoned, neglected or abused.

“These are children,” said McKenna. “If they are kept in a Border Patrol facility and asked questions, it’s going to be very hard for them to talk about what’s happened to them. They’ve just come out of the desert without a parent or legal guardian, and in many cases these children are also abused on the journey here.”

Many who are released from HHS’s supervision are referred to groups such as KIND, which has handled more than 6,000 children, including some as young as 2 years old.

“They say they feel they have to leave their countries or die,” McKenna said. “The majority say they were targeted by violent gangs and cartels. There is very little state protection in these countries.”

But some say that HHS is ill-prepared to handle the crisis – and, they argue, the federal government is unfairly being burdened by the sudden mass of children illegally crossing the border.

“I am deeply concerned with HHS’ lack of transparency and preparation…,” Rep. James Sensenbrenner Jr. (R-Wis.) wrote in a letter to HHS. “Where is HHS currently housing UACs and for how long? What other sites/locations are currently planned? What do you anticipate to be the final cost of housing UACs to taxpayers?”

Obama is seeking about $2 billion to respond to the flood of immigrants illegally entering the U.S. through the Rio Grande Valley area of Texas and ask for new powers to deal with returning immigrant children apprehended while traveling without their parents.

Details of the emergency appropriation, including the exact amount and how it will be spent, will come after lawmakers return from their holiday recess on July 7, according to published reports.

Obama also is asking that the Homeland Security Department be granted the authority to apply "fast track" procedures to the screening and deportation of all immigrant children traveling without their parents and that stiffer penalties be applied to those who smuggle children across the border.

“It’s an emergency response and everyone is doing best they can,” McKenna said. “These children are potentially very traumatized. We’re concerned the system is breaking down.”